Method and Apparatus for Creating a Computer Simulation of an Actor

ABSTRACT

A method for creating a computer simulation of an actor having a first foot, a second foot and a body including the steps of planting the first foot as a support foot along a space time-varying path. There is the step of stopping time regarding placement of the first foot. There is the step of changing posture of the first foot while the first foot is planted. There is the step of moving time into the future for the second foot as a lifted foot and changing posture for the lifted foot. An apparatus for creating a computer simulation of an actor having a first foot, a second foot and a body. A software program for creating a computer simulation of an actor having a first foot, a second foot and a body that performs the steps of planting the first foot as a support foot along a space time-varying path.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 13/569,947filed on Aug. 8, 2012, now U.S. Pat. No. 9,251,617, which is acontinuation of U.S. patent application Ser. No. 11/361,748 filed Feb.24, 2006, now U.S. Pat. No. 8,243,078 issued Aug. 14, 2012, which claimspriority from U.S. provisional patent application Ser. No. 60/657,269filed Feb. 28, 2005, all of which are incorporated by reference herein.

FIELD OF THE INVENTION

The present invention is related to creating a computer simulation of anactor. More specifically, the present invention is related to creating acomputer simulation of an actor which computes joint values byevaluating a plurality of modules which compute positions andorientations for feet and ankles, hands reaching/grasping, pelvis andspine and neck, hands swinging, legs and arms, and head gaze of theactor to accommodate dependencies between computations for differentparts of the actor.

BACKGROUND OF THE INVENTION

The first computer graphic system to do 3D keyframe based human jointanimation was a pure kinematic system introduced by [STERN, G., 1978.Garlands animation system (gas) a system for computer-aided keyframeanimation. Doctoral Thesis, incorporated by reference herein], in whichhand-made static poses were interpolated by smooth splines. Since then,there has been much work on automating the computer simulation of 3Dwalking characters. This work has variously focused on kinematics anddynamics.

The first high level parameterized kinematic based automation of walkingwas done by [ZELTZER, D., 1982. Motor Control Techniques for FigureAnimation. IEEE Computer Graphics and Applications, 2(9):53-59,incorporated by reference herein]. Hierarchical concurrent statemachines were used to control the gait of a synthetic skeleton. Apre-defined key posture was associated with each FSM state. Transitionsbetween states produced linear interpolations between key-postures,producing joint angles that drove the animation.

Bruderlin and Calvert [BRUDERLIN, A., and CALVERT, T., 1989.Goal-directed, dynamic animation of human walking, In Computer Graphics(Proceedings of ACM SIGGRAPH 89), 23, 4, ACM, incorporated by referenceherein] achieved non-slip foot placement by making the contact foot theroot of the kinematic chain, and treating it as an inverted pendulum.They later combined this approach with parameterizable styles of walking[BRUDERLIN, A., and CALVERT, T., 1993. Interactive Animation ofPersonalized Human Locomotion. In Proc. of Graphics Interface 93, pages17-23, incorporated by reference herein].

Boulic [BOULIC R., MAGNETAT-THALMANN, N., and MAGNETAT-THALMANN, D.,1990. A global human walking model with real-time kinematicpersonification. Visual Computer, 6(6):344-358, incorporated byreference herein] used forward kinematics followed by an inversekinematics post-processing step to modify foot position when feetpenetrated the ground, and then later modified this approach to maintainproper balance centering of the body over the feet [BOULIC, R., MAS, R.,and MAGNETAT-THALMANN, D., 1996. A robust approach for the center ofmass position control with inverse kinetics. Journal of Computer andGraphics, 20(5), incorporated by reference herein].

Ko and Badler [KO, H. and BADLER, N., 1996. Animating Human Locomotionin Real-time using Inverse Dynamics, Balance and Comfort Control. IEEEComputer Graphics and Applications, 16(2):50-59, incorporated byreference herein] did post-processing inverse dynamics on kinematicwalking, adjusting the results of forward kinematics to ensure thatmovement embodied appropriate forces. Spacetime constraints on the bodycenter were introduced by Witkin [WITKIN, A. and KASS, M., 1988. InComputer Graphics (Proceedings ofACM SIGGRAPH 88), 22, 4, ACM,incorporated by reference herein] to compute these correcting dynamics,specified as the minimization of a cost function, over the entire courseof an animation, rather than sequentially in time. Cohen [COHEN, M.,1992. Interactive spacetime control for animation. In Computer Graphics(Proceedings of ACM SIGGRAPH 92), 26, 4, ACM, 293-302, incorporated byreference herein] refined this approach to allow space-time windows tobe specified, so that these dynamic adjustments could be appliedinteractively. Gleicher [GLEICHER, M., 1997. Motion editing withspacetime constraints. In Proc. of Symposium on Interactive 3D Graphics,incorporated by reference herein] extended space-time constraints to thehandling of constraints on all kinematic trajectories of the walkingfigure.

SUMMARY OF THE INVENTION

The present invention pertains to a method for creating a computersimulation of an actor having a first foot, a second foot and a body.The method comprises the steps of planting the first foot as a supportfoot along a space time-varying path. There is the step of stopping timeregarding placement of the first foot. There is the step of changingposture of the first foot while the first foot is planted. There is thestep of moving time into the future for the second foot as a lifted footand changing posture for the lifted foot.

The present invention pertains to an apparatus for creating a computersimulation of an actor having a first foot, a second foot and a body.The apparatus comprises a computer. The apparatus comprises a softwareprogram that performs the steps of planting the first foot as a supportfoot along a space time-varying path. There is the step of stopping timeregarding placement of the first foot. There is the step of changingposture of the first foot while the first foot is planted. There is thestep of moving time into the future for the second foot as a lifted footand changing posture for the lifted foot.

The present invention pertains to a software program for creating acomputer simulation of an actor having a first foot, a second foot and abody that performs the steps of planting the first foot as a supportfoot along a space time-varying path. There is the step of stopping timeregarding placement of the first foot. There is the step of changingposture of the first foot while the first foot is planted. There is thestep of moving time into the future for the second foot as a lifted footand changing posture for the lifted foot.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, the preferred embodiment of the inventionand preferred methods of practicing the invention are illustrated inwhich:

FIG. 1 is a block diagram of the inputs and outputs with respect to thepresent invention.

FIG. 2 is a graph of a saw function.

FIG. 3a shows variations in limb length.

FIG. 3b shows variations in stance.

FIG. 3c shows two link inverse kinematics.

FIG. 3 shows the three time frames.

FIG. 4 shows a crouch backwards, turn sideways.

FIG. 5 shows descending steps.

FIG. 6 shows shifting phase for stairs.

FIG. 7 shows transition to/from broadjump.

FIG. 8 shows a varying skeleton.

FIG. 9 shows shuffling to Gollum to Sultriness.

FIG. 10 shows two application modes.

FIGS. 11a and 11b show camera fly-through and featured dancer.

FIG. 12a and FIG. 12b show artificial intelligence agents andcorresponding actors.

DETAILED DESCRIPTION

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIGS. 3a, 3b and 3c thereof, there is shown a method forcreating a computer simulation of an actor having a first foot, a secondfoot and a body. The method comprises the steps of planting the firstfoot as a support foot along a space time-varying path. There is thestep of stopping time regarding placement of the first foot. There isthe step of changing posture of the first foot while the first foot isplanted. There is the step of moving time into the future for the secondfoot as a lifted foot and changing posture for the lifted foot.

Preferably, there is the step of alternating the first and second feetover a walk cycle having a first half and a second half, so that thelifted second foot switches roles with the planted first foot and theplanted first foot switches roles with the lifted second foot of thefirst half during the second half of each walk cycle. There ispreferably the step of creating emotionally expressive postures for thebody. Preferably, the space-time path is a function of parameters whichcontain values for a rude positioned X, Y, of the actor, and values fora plurality of postural parameters of the actor.

The postural parameters preferably include how far apart the actor'sfeet are, the degree of bending of the actor's knees, how far back theactor's shoulders are, and how much the actor's hips are swaying fromside to side when the actor is walking.

Preferably, the space-time path is implemented as a set of key frames atdiscrete values of time. Preferably, there is the step of convertingpath values to joint values. The converting step preferably includes thestep of examining key frames along the path that influence values withina window of time that contains one walking length of the actor.

Preferably, there is the step of computing joint values by evaluating aplurality of modules which compute positions and orientations for feetand ankles, hands reaching/grasping, pelvis and spine and neck, handsswinging, legs and arms, and head gaze of the actor to accommodatedependencies between computations for different parts of the actor.

The present invention pertains to an apparatus for creating a computersimulation of an actor having a first foot, a second foot and a body.The apparatus comprises a computer. The apparatus comprises a softwareprogram that performs the steps of planting the first foot as a supportfoot along a space time-varying path. There is the step of stopping timeregarding placement of the first foot. There is the step of changingposture of the first foot while the first foot is planted. There is thestep of moving time into the future for the second foot as a lifted footand changing posture for the lifted foot.

Preferably, there is the step of alternating the first and second feetover a walk cycle having a first half and a second half, so that thelifted second foot switches roles with the planted first foot and theplanted first foot switches roles with the lifted second foot of thefirst half during the second half of each walk cycle. There ispreferably the step of creating emotionally expressive postures for thebody. Preferably, the space-time path is a function of parameters whichcontain values for a rude positioned X, Y, of the actor, and values fora plurality of postural parameters of the actor.

The postural parameters preferably include how far apart the actor'sfeet are, the degree of bending of the actor's knees, how far back theactor's shoulders are, and how much the actor's hips are swaying fromside to side when the actor is walking.

Preferably, the space-time path is implemented as a set of key frames atdiscrete values of time. Preferably, there is the step of convertingpath values to joint values. The converting step preferably includes thestep of examining key frames along the path that influence values withina window of time that contains one walking length of the actor.

Preferably, there is the step of computing joint values by evaluating aplurality of modules which compute positions and orientations for feetand ankles, hands reaching/grasping, pelvis and spine and neck, handsswinging, legs and arms, and head gaze of the actor to accommodatedependencies between computations for different parts of the actor.

The present invention pertains to a software program for creating acomputer simulation of an actor having a first foot, a second foot and abody that performs the steps of planting the first foot as a supportfoot along a space time-varying path. There is the step of stopping timeregarding placement of the first foot. There is the step of changingposture of the first foot while the first foot is planted. There is thestep of moving time into the future for the second foot as a lifted footand changing posture for the lifted foot.

Preferably, there is the step of alternating the first and second feetover a walk cycle having a first half and a second half, so that thelifted second foot switches roles with the planted first foot and theplanted first foot switches roles with the lifted second foot of thefirst half during the second half of each walk cycle. There ispreferably the step of creating emotionally expressive postures for thebody. Preferably, the space-time path is a function of parameters whichcontain values for a rude positioned X, Y, of the actor, and values fora plurality of postural parameters of the actor.

The postural parameters preferably include how far apart the actor'sfeet are, the degree of bending of the actor's knees, how far back theactor's shoulders are, and how much the actor's hips are swaying fromside to side when the actor is walking.

Preferably, the space-time path is implemented as a set of key frames atdiscrete values of time. Preferably, there is the step of convertingpath values to joint values. The converting step preferably includes thestep of examining key frames along the path that influence values withina window of time that contains one walking length of the actor.

Preferably, there is the step of computing joint values by evaluating aplurality of modules which compute positions and orientations for feetand ankles, hands reaching/grasping, pelvis and spine and neck, handsswinging, legs and arms, and head gaze of the actor to accommodatedependencies between computations for different parts of the actor.

In the operation of the invention, when creating complex softwaresimulations or computer games, it is useful to incorporate virtualactors that simulate the appearance of human behavior while movingwithin the simulated environments. It can be difficult to reconcileproper foot placement with the full range of body postures needed toconvey emotion and attitude, without compromising quality of movement.Both posture and foot placement should ideally anticipate the higherlevel goals and intentions of the actor, and should vary according towhat the actor's goals are at higher cognitive levels.

The current invention recasts the movement of these virtual actors as afunction of a path of values through time (rather than simply throughspace). This allows an approximate simultaneous solution to beconstructed to the problems of (1) choosing good foot placement and (2)creating emotionally expressive body postures, in a way that simplifiesand unifies these two sub-problems.

The key insight is to look at all body parameters along thistime-varying path, and then to consider the actors support foot andlifted foot as though they are traveling along the same time-varyingpath as the rest of the body, only at variable rates. For the supportingfoot planted on the ground, time stops and posture is frozen. For thelifted foot, time accelerates into the future and posture changesrapidly.

Such a framework allows all aspects of body posture to be controlled byefficiently computed algorithmic procedures which can be evaluated at asingle point in time, in much the way that “procedural shaders” used forprocedural texture synthesis can be evaluated at a single point in space[PERLIN, K., 1985. An Image Synthesizer, In Computer Graphics(Proceedings of ACM SIGGRAPH 85), 19, 4, ACM, incorporated by referenceherein].

The result is not biomechanically perfect, but it is extraordinarilyfast and flexible. This mechanism provides a framework in whichprogrammers can create algorithmic mechanisms for the control of virtualactors which enable artists to exert very fine control over characterattitude and emotion via the use of simple and intuitive parameters.Hundreds of actors can be interactively directed in real-time onconsumer level hardware, with each displaying emotively convincing bodylanguage and proper foot placement. These actors can be made toprecisely follow arbitrary paths, including uneven terrain and stairs,with equal facility in all walk styles.

Even when virtual actors possessing a higher degree of biophysicalaccuracy are required, virtual actors constructed using this mechanismcan serve as a highly controllable and expressive instrument to createapproximate solutions that feed into more computationally heavyconstraint optimization and energy minimization techniques.

The computational framework of the present technique is based onspace-time paths. Let space-time path P(time) V be a function that mapstime to a vector of parameter values V. In practice, V will containvalues for the root position x, y, and z of the actor, as well as valuesfor a plurality of postural parameters.

Typical examples of such parameters are: how far apart the feet are, thedegree of bending at the knees, how far back the shoulders are set, howmuch the hips sway from side to side when walking.

A function ACTOR(P,M,T,time)→J is defined which takes as input:

(1) a space-time path P;

(2) a set of constant body metrics M, which includes such bodymeasurements as forearm length, thigh length and torso length;

(3) a set of target points T in the environment, which includes the gazefixation point and the positions of objects to be grasped by the virtualactor;

(4) a value for time; and produces as its output a set of joint matricesJ (FIG. 1).

In practice, the space-time path P(time) is implemented as a set ofkey-frames at discrete values of time. The values at other intermediatepoints in time are interpolated by continuous interplolant such aspiece-wise cubic splines or piece-wise linear functions.

The virtual actor converts path values to joint values. To do this atany given time, the actor needs to examine keyframes along the path thatinfluence values within the window of time that contains one walkingstride length.

For a human figure, the actor function computes joint values byevaluating the following six modules in the indicated order, toaccommodate dependencies between computations for different parts of thesimulated human body:

1. Feet+Ankles

2. Hands reaching/grasping

3. Pelvis+Spine+Neck

4. Hands swinging

5. Legs+Arms

6. Head Gaze

Note that the hands are visited in two different modules. Reaching andgrasping are computed before the pelvis and spine, whereas hand positionfor arm swinging is computed after the pelvis and spine.

In order for the body to be emotionally expressive, the spine needs tobe sufficiently flexible. In one embodiment the spine is represented bythe five joints corresponding to the fifth and first lumbar vertebrae(the lower back), the sixth thoracic vertebrae (the chest cage) and thefifth and first cervical vertebrae (the base and top of the neck).

After the pelvis, torso and feet positions have been computed, thepelvis is connected to the feet, and the torso is connected to thehands, via a simple closed-form two-link inverse kinematics computationwhich positions the knees and elbows. Both knee and elbow turn-outangles default to values that appear natural. Deviations from thesevalues are then parametrically adjustable by the artist.

All of the modules receive a value of time as their input except for themodule that computes the foot positions and ankle joints. The left footis given an altered time input value of:

time+saw(time/pace)

whereas the right foot is given an altered time input value of:

-   -   time+saw(time/pace+½)

where pace is in units of walk cycles per second, and saw(t) is definedby:

saw(t)=if (t mod 1)<½ then (t mod 1)−¼ else ¾−(t mod 1) (FIG. 2)

The effect of this time displacement is to jog time back and forth inthe course of a single walk cycle. In the first half of the walk cyclethe left foot travels forward in time one full cycle, while the rightfoot remains fixed at the start of the cycle. In the second half of thewalk cycle, the right foot travels forward in time one full cycle, whilethe left foot remains fixed at the end of the cycle, as in FIG. 3.

The one exception to the above is the continuous heel-to-toe foot rollof the support foot while that foot is in contact with the floor. Eventhough the values of all body parameters are fixed in time while thesupport foot is in contact with the floor (because time is not changingwhile the foot is in contact with the floor), the mechanism nonethelesscontinues the rotation of the foot that produces the rolling floorcontact for first the heel, then the ball of the foot, and finally thetoe. The bending at the metatarsal during the last stages of floorcontact is handled as a simple kinematic constraint: the front part ofthe foot is bent a sufficient angle so that it will not penetrate thefloor. When the virtual actor is walking backwards, proceed similarly,but reverse the direction of roll: the toe contacts the floor first, andthen the foot rolls onto the heel.

Because the entire mechanism is a function of (1) fixed body metrics,(2) the space-time path, and (3) target points T, any given collectionof values for these will produce a unique and well defined set of valuesfor the collection of joints J at a given time.

This mechanism confers several desirable properties on the resultinganimation. Because reasonable foot placement is guaranteed, theprogrammer working within this framework to create parametric controlsfor artists is free to implement any desired mechanism for control ofbody posture. The artist using such mechanisms can blend expressivemovements in a preferred parameter space, through the use of parametriccontrols which are intuitive and easy to work with.

For a walking biped, the placement of the skeletal limbs from the pelvison down (the pelvis, upper legs, lower legs, and foot parts) areinter-related. The described temporal phase-shift mechanism makes iteasier to place the pelvis and the parts below it in a way that iscoordinated and appears natural.

In this section, the degrees of freedom of these lower body parts areenumerated, and the mechanisms to place them are described.

All of the body parts of a walking biped from the pelvis downward areinvolved in foot placement. The actual positions are of the body partsare dependent upon three types of numerical quantity:

-   -   Limb lengths    -   Parameters controlling stance    -   Parameters varying position during the walk cycle

Of the above, limb lengths are generally unchanging throughout time. Thestandard limb lengths that influence the placement of body parts of abiped from the pelvis down are shown in FIG. 3 a.

Parameters controlling stance and parameters varying position during thewalk cycle influence the same degrees of freedom. The only difference isthat the latter cause rhythmic changes to these degrees of freedom overthe cause of each successive walk cycles. The degrees of freedom whichare influenced are shown in FIG. 3 b.

In one embodiment, the placement of the two feet at a known time for abipedal virtual actor walking at a constant speed and a known pace (asmeasured in cycles per second), along a straight line path with a knownfoot lift can be described as follows:

Walk Cycle:

offset=if left_foot then 0.0 else 0.5

phase=time/pace+offset

foot_forward=speed×saw(phase)

foot_lifted=lift×max(0, sin(2 πp phase))

In other embodiments, the sin( )function, which serves as a periodictime-varying control of elevation of each foot above the ground, can bereplaced with a different periodic function.

The degrees of freedom which can vary positioning of lower body parts inwalking at a constant rate along a straight-line path can be enumeratedas follows. For some of these degrees of freedom, such as the amountthat a foot turns inward or outward, it is reasonable to assign positiveand negative values (i.e.: range=−1 . . . 1). For others, such as theamount that the feet lift off of the floor when walking, it is onlyreasonable to assign positive values (i.e.: range=0 . . . 1).

parameter range Limb lengths: Hip width   0 . . . 1 L femur length   0 .. . 1 R femur length   0 . . . 1 L tibia length   0 . . . 1 R tibialength   0 . . . 1 L foot length   0 . . . 1 R foot length   0 . . . 1Pelvis movement: Up (i.e.: knees straight)   0 . . . 1 Lean to side −1 .. . 1 Thrust back or forward −1 . . . 1 Tilt back or forward −1 . . . 1Turn left or right −1 . . . 1 Roll left or right −1 . . . 1 Legplacement: L knee turn out −1 . . . 1 R knee turn out −1 . . . 1 Footplacement: L ankle turn out −1 . . . 1 R ankle turn out −1 . . . 1 Rankle roll to side −1 . . . 1 R ankle roll to side −1 . . . 1 L ankletilt heel to toe −1 . . . 1 R ankle tilt heel to toe −1 . . . 1 L footmove to side   0 . . . 1 L foot move to side   0 . . . 1 Other: Hop onone foot −1 . . . 1 Pace of walk   0 . . . 1 Foot lift for walk   0 . .. 1 Sidling walk −1 . . . 1

Because the position of the top of the femur and the position of thebottom of the tibia are completely determined by parameters controllingthe position of the hips and ankles, there is only one additional degreeof freedom per leg in the stance of the biped: the degree of knee turnout, as shown above.

All of the above pose variations are described with respect to the rootcoordinate frame of the walking virtual actor. This coordinate frame isitself moving in a straight line so that the virtual actor appears totravel forward.

The six degrees of pelvis variation consist of three degrees oftranslational freedom and three degrees of rotational freedom. These canall be described by a single affine transformation, which can beexpressed as a 4×4 transformation matrix.

The position and orientation of each ankle for a biped walking at aconstant speed along a straight line are completely determined by thethree parameters that control its time-varying position: foot forward,foot lifted and foot move_to_side, and the three parameters that controlthe ankle orientation: turn out, roll to side and tilt to tiptoe. Giventhese values, the position and orientation of each foot can be expressedby a 4×4 transformation matrix.

Once the position and orientation of pelvis, left foot and right footare determined, there is only one remaining degree of freedom left forplacing each leg: the degree of rotational turn-out at the knee. Thesecan be specified by time-varying parameters Left knee turn-out and Rightknee turn-out. Given the value of knee turn-out, each leg can be rigidlypositioned as a simple closed-form solution to the two-link inversekinematics chain of hip→? knee→? ankle, as follows:

Given a hip located at the origin, respective femur and tibia lengths aand b, and an ankle located at point D, there is only one remainingdegree of freedom: the rotation of the knee position around the axisthat runs from the origin through D. This rotation can be specified byspecifying some point C that lies in plane that contains both the kneeand this axis. Given a, b, C and D, knee position K can be computed asfollows (FIG. 3c ):

x=½+½(a ² −b ²)/(C·C)

E=D-−C (C·D)/(C·C)

K=Cx+E ✓v max(0, a ²-−(C·C)x ²)/E≠E

Walking Along Arbitrary Space-Time Paths with No Foot-Slip

The above section describes how to place the pelvis, knees and feet as abipedal virtual actor walks along a straight line path at a constantrate, with all parameters fixed to a constant value. If the path were tochange to a curved path, or the rate of forward movement were to varythrough time, or if there is any variation through time of theparameters which control limb length, stance or changing positionthroughout the walk cycle, then the support feet would appear to slip onthe floor, thereby destroying the visual illusion that the virtualactor's support foot is properly affixed to the floor for that portionof the walk cycle during which the support foot carries the weight ofthe virtual actor.

If all controlling parameters are described within a space-time path asdescribed earlier, and if the novel mechanism is used of employingtemporal variation along this path, also described earlier, then thesupport foot does not slip on the floor, but rather stays in aconsistent position with respect to the world, until the foot is lifted.While on the ground, the support foot linearly transitions from beinghalf a cycle in the future to being half a cycle in the past, withrespect to the pelvis of the virtual actor.

In addition, the lifted foot automatically moves along a path thatappears to show the higher level cognitive intentionality of the virtualactor, because this lifted foot literally moves into the future (i.e.:forward in time along the space-time path), thereby anticipating thevirtual actor's intentions as expressed in time-varying values for actorlocation, stance and changing position throughout the walk cycle. As theanimation progresses, and this lifted foot thereby descends and becomesthe next support foot, the foot is placed in a position and orientationwhich is consistent with the movements of the virtual actor for the nexthalf cycle. While in the air, the lifted foot linearly transitions frombeing half a cycle in the past to being half a cycle in the future, withrespect to the pelvis of the virtual actor.

AN EXAMPLE

In the sequence shown in FIG. 4, a walking virtual actor has beendirected first to crouch backwards, and then to turn sideways with feetspread, before continuing on his way. To create this behavior, theartist simply specifies a keyframe (corresponding to the fourth image ofFIG. 4) in which the actors pelvis should be lowered and rotated by 180,and then a keyframe (corresponding to the eighth image of FIG. 4) inwhich the actors feet should be spread and the pelvis rotated 90. In thecourse of executing this transition, the actor produces a trajectory forthe feet and for all body joints (seen in images two and three, andimages five through seven) that results in reasonable foot placement andno foot sliding. This will be true for any walking pace and for allsettings of other body parameter values.

Uneven Terrain and Walking Up and Down Stairs

Reasonable foot placement when walking along uneven terrain isautomatically guaranteed by the periodic temporal displacement appliedto the feet that has been described above. Since the pelvis and the twofeet exist in three different time frames, within its own respectivetime frame, each of these three body parts simply maintains the propervertical distance above whatever is the current terrain height for thatrespective part at that moment in time. The result is a walk in whichthe pelvis maintains a proper distance from the ground, and the feetland at ground level of the varying terrain at each footfall. As in[ROSE, C. COHEN, M, and BODENHEIMER, B., 1998. Verbs and Adverbs:Multidimensional Motion Interpolation. IEEE Computer Graphics andApplications, 18(5):32-40, incorporated by reference herein], adverbialparameter settings to convey change in stance when climbing ordescending are blended in. Rose refers to these blended in settings as“adverbs”. This blending is described below in further detail. Incontrast, walking up or down stairs requires some intervention, so thatthe actor will walk upon the stair steps, rather than upon the risesbetween steps, which are height discontinuities that separate successivestair steps.

In order to ensure that the virtual actor walks up and down stepsproperly, the basic algorithm is modified to allow the pace of the actorto vary, so that the actor's feet will land on the stair steps, ratherthan between them. In FIG. 5, the actor is portraying a slitheringcreature skulking down stairs. The height of the actors pelvis above thefloor is computed by blurring the terrain height function (in this case,via a MIPmap [WILLIAMS, L., 1983. Pyramidal Parametrics. In ComputerGraphics (Proceedings of ACM SIGGRAPH 83), 17, 4, ACM, incorporated byreference herein]). The higher the pelvis, the blurrier is the effectiveheight function. This results in smooth movement of the pelvis overstair steps as well as over any other discontinuities in floor height.

The floor height at each foot is only evaluated at places where thatfoot touches down; that is, where the phase of the walk cycle is amultiple of 0.5 cycles.

The actor's feet are guaranteed to land on the steps, not on the risesbetween steps, by shifting the phase slightly at the keyframes. In anapproach similar to [CHUNG, S., and HAHN J., 1999. Animation of HumanWalking in Virtual Environments. In Proc. Int. Conf. on ComputerAnimation, pages 4-15. IEEE, incorporated by reference herein],preparation is started for the step up or down two keyframes ahead. Thisgives enough time to smoothly and unobtrusively modify the footstepphase before the edge of a stair-step. The algorithm is illustrated inFIG. 6. The keyframes themselves (shown in the diagram as circularrings) are not moved, but the walk-cycle phase at each keyframe isadjusted slightly, so that each of the places where the left foottouches down (where phase is a multiple of 1.0 cycles), and where theright foot touches down (where phase is an odd multiple of 0.5 cycles)is shifted to the center of a stair step. This process is independent ofstyle parameters: the actor can go up and down stairs equally well inany walking style.

In the context of producing a linear animation, it is important to beable to effect such phase shifts locally, without changing the phase ofthe walk cycle at all later points in the animation. In this way theanimator can be sure that foot placement does not change unexpectedly inlater scenes due to edits in earlier scenes. To this end, the phaseshifting mechanism always takes care to localize any imposed phaseshifts, such as those caused by negotiating stairs. In this way, theoriginal walk cycle phase is restored after a small number of additionalkeyframes.

Staggered Gaits

This approach to walking movement facilitates the creation of staggeredwalks or gaits, by providing control over the amount of temporal phasedisplacement between the two feet. For example, a character cantransition from a walk to a broadjump by changing the temporal phasedifference between the two feet (normally half a cycle) gradually tozero. FIG. 7 shows a transition first into, and then out of, abroadjump. By setting the phase displacement to intermediate values, theactor can be made to perform staggered or skipping gaits.

Similarly, the appearance of heavy steps or light steps, as defined bythe percentage of time that each foot remains in contact with theground, can be modulated by sinusoidally modulating each foots temporalphase displacement throughout the period of the walk cycle. In this way,footsteps can be made heavy (more time spent in fixed support, as wouldbe found if an actor were wearing lead shoes), or light (both feet offthe ground simultaneously, as would occur while running).

Variation in Body Skeleton

Because the behavior of the parameters which modulate body posture isnot constrained by any special requirement to accommodate footplacement, it is easy and straightforward in practice to implement thealgorithms that vary these parameters in a way that is insensitive tothe lengths of the various limbs. A virtual actor can have very long orshort legs, unequal lengths between the femur and tibia, long or shortspine, or a very wide or narrow pelvis. The knees can just as easilybend backwards, which is useful for actors playing avian characters.Limb length can change in the middle of an animation, which can beuseful in certain exaggerated cartoon contexts. This allows a resultsimilar to the motion retargeting of [GLEICHER, M., 1998. RetargetingMotion to New Characters, In Proceedings of ACM SIGGRAPH 1998 ACMPress/ACM SIGGRAPH, New York. Computer Graphics Proceedings, AnnualConference Series, ACM, incorporated by reference herein], but atsmaller computational cost. FIG. 8 shows several examples of highlydivergent actors performing the same movement.

Integrating with Body Posture

The foot animation system is part of a larger framework. In thisframework, animation shaders add attitude to the entire body posture andmotion. The following descriptions of motion idioms and posturevariation describe how the enabling mechanism benefits the constructionof full body postures.

Motion Idioms

The integration of footstep placement and body posture adjustmentsimplifies the creation of parameters to vary body posture. This makesit much easier to construct body posture variation which is intuitive toan artist or animator who wishes to control the virtual actor.

The use of intuitive body attitude parameters facilitates the simplecreation of “idioms”—combinations of static and rhythmic posture thatcreate a characteristic higher level mood or attitude. For example, inthe one embodiment a parameter is provided that sinusoidally varies thepelvis height at twice the frequency of the walk cycle, so that thepelvis rises each time a support foot strikes the ground. This creates abouncy gait, which conveys an appearance of carefree walking motion. Ifthis same parameter is set to a negative value, then the pelvis descendseach time a support foot strikes the ground. This produces theappearance of a jaunty, bopping style of walk. In this latter case, theimpression of bopping is greatly enhanced by making the footsteps heavy,as described above, so that the actor appears to be deliberately placingeach footstep. A negative bounce together with a heavy step can bemerged into a single combination “bop” parameter, in which these twodegrees of freedom are varied together.

Similarly, it is straightforward to create parameter combinations thatsuggest such attitudes as fearful, sexy, careful, or slithering. Suchcombinations can be saved and then blended with various weights duringthe course of an animation or simulation, to suggest subtle momentarymoods and attitudes. This is similar in spirit to the interpolationapproaches described by [PERLIN, K., 1995. Real Time ResponsiveAnimation with Personality, IEEE Transactions on Visualization andComputer Graphics; Vol 1 No. 1; WILEY, D. and HAHN, J., 1997.Interpolation Synthesis of Articulated Figure Motion, IEEE ComputerGraphics and Applications, 17(6):39-45; ROSE, C. COHEN, M, andBODENHEIMER, B., 1998. Verbs and Adverbs: Multidimensional MotionInterpolation. IEEE Computer Graphics and Applications, 18(5):32-40, allof which are incorporated by reference herein]. One difference is thatthe described mechanism automatically computes proper foot placement forthe interpolated movement.

For example, in one embodiment a walk with a sultry appearance can bedefined by setting a small number of parameters: bring the elbows in,feet together, heels up, pelvis and shoulders forward, increase the armswing and vertical pelvis bounce, and increase both the sway and axialrotation of hips and shoulders. The resulting walk automatically findsproper footfall positions for any path the virtual actor is directed tofollow. In practice, fractional quantities of body language shadingssuch as sultriness can be mixed into an actor momentarily, as when acharacter is behaving in a seductive manner in order to catch the eye ofanother character.

In the sequence shown in FIG. 9, the virtual actor transitions betweenseveral idiomatic behaviors in a the span of a few steps: first from ashuffling old man, to a feral Gollum-like creature; then to a sultrywalk. To create this sequence it was necessary only to specify theappropriate idiom at successive key frames. The original creation ofeach of the three component idioms required only a few minutes ofparameter adjustment by an artist.

Types of Posture Variation

Posture parameters have been selected to provide intuitive isolatedcontrols over those attributes of posture of a virtual actor that atrained actor or dancer might wish to independently modulate during aperformance. A parameter can be either static, rhythmic, or stochasticStatic parameters are those which are insensitive to the phase of thewalk cycle. These include such postural properties as spacing betweenthe feet, amount of bending at the knee, how much the toes are pointed,the axial twist of the pelvis, and how far forward or back the pelvis isthrust. Rhythmic parameters include amplitude of rolling shoulders orhips, the vertical bounce and thrust of the pelvis during the walkcycle, and the amplitude of arm swing. Stochastic parameters arepostural parameters that are varied through time using a continuouspseudo-random function such as Perlin Noise [PERLIN, K., 1985. An ImageSynthesizer, In Computer Graphics (Proceedings of ACM SIGGRAPH 85), 19,4, ACM, incorporated by reference herein].

Blending Posture Parameters

As in [ROSE, C. COHEN, M, and BODENHEIMER, B., 1998. Verbs and Adverbs:Multidimensional Motion Interpolation. IEEE Computer Graphics andApplications, 18(5):32-40, incorporated by reference herein], higherlevel parameter settings are mixed in as adverbs to convey a temporarychange in a virtual actor's attitude when the virtual actor is beingdirected to perform a difficult or interesting task. For example, whenthe virtual actor is climbing or descending stairs, parameter settingsare fractionally blended in to convey the idiomatic appearance of morecareful and deliberate balancing (arms slightly raised, elbows out, feetapart and turned out, pelvis slightly lowered, shoulders hunched andforward, spine curved forward, heavy steps, slightly wandering gaze,slight wandering of path, slow pace, slightly staggered foot rhythm,high shakiness, very little movement in the hips). When reduced topractice, the resulting performance is surprisingly compelling.

APPLICATION

Production Advantages: Frame-Independent Evaluation and Path Following

Like any system that is based on a closed-form kinematic solution, thecomplete pose of the actor is a function of time which can be evaluatedefficiently at any single input value of time. This confers thedesirable properties that (1) the computation does not depend uponforward differencing between successive values of time, and (2) there isno variation in the behavior or body posture of the virtual actor due tovariable animation frame rate, as defined in computations per second.Any individual frame in an animation can be computed and examinedindependently. Body posture and foot placement are completely determinedand repeatable. This is a highly desirable property in a productionanimation setting, and a notable benefit of the current invention.

In addition, the path following is precise: the virtual actor isguaranteed to follow the exact path laid out by the specified keyframes.This is extremely important in situations containing tight physicalconstraints such as narrow doorways and hallways or tightly packedcrowds. Precise path following is also essential for the use of virtualactors in implementing dance choreography, as well as in dramatic scenesin which the virtual actor needs to accurately hit its mark so that itwill be properly framed in the camera shot. By analogy with thedifferent components of the human brain, the virtual actor isconstrained to function as pure cerebellum—implementer of externalcognitive choices. All actual cerebral cognitive decisions are directedby the animator or A.I. engine, and conveyed to the virtual actor withinthe parameter settings of successive keyframes.

Linear Animation Versus Real-Time Simulation

There are at least two distinct types of environments in which thedescribed mechanism can be used: (1) the design of linear animation witha fixed set of key frames, and (2) interactive simulations, in whichstreams of key frames are continually provided by an A.I. program.

The body animation system itself, which is the embodiment of the currentinvention, is identical in both environments. This subsystem is alwaystasked with converting data from a small time window of keyframes intojoint matrices. The difference between (1) and (2) lies entirely in thesource of the keyframe data. For hand-tuned linear animation, parameterswithin a fixed set of keyframes are altered by a skilledanimator/director. For interactive simulations, a moving window oftemporary keyframes is generated by programs written by the A.I.designer of a game or simulation engine. (FIG. 10)

Interactive Crowd Simulation

The use of the described mechanism allows A.I. for a crowd simulation tobe computed without any knowledge of the body animation system. Becausethe virtual actors are guaranteed to follow their marks precisely, it ispossible to articulate large numbers of virtual actors withoutcollisions and with repeatable results: each walking virtual actor willprecisely follow the output position of the corresponding agent in theA.I. that directs the crowd.

In one embodiment interactive scenes containing 1000 dancing virtualactors have been implemented, with the entire animation, including bothbehavior and rendering computations, updating nine times per second. Inthis implementation the keyframe parameters for each virtual actor wererandomized, so that each virtual actor dances with a unique personalityand character. In FIG. 11a , a virtual computer graphic camera is flyingthrough the crowd simulated in this implementation. As the cameraapproaches, the individual virtual actors in the camera's path turntoward the camera and dance out of the way, creating an aisle for thecamera to travel through. In FIG. 11b , the crowd has made space for alone dancer at center stage.

All of the behavior for the scene described above was computed via aseparate 2D crowd simulation. FIGS. 12a and 12b show, side by side, avisualization of just the A.I. for that crowd simulation (FIG. 12a ),and then of the virtual actors who are taking their position cues fromthat A.I. (FIG. 12b ). For each virtual actor, the individual bodyposture, limb positions and foot placement are computed in a jointsynthesis system enabled by this invention.

Performance

Because the described mechanism enables a closed-form mapping fromparameters and target points to joint matrices, computation speed doesnot depend upon input values. In one embodiment, animated crowdsconsisting of up to 1000 interactive responsive virtual actorssimultaneously, with each virtual actor set to a different setting ofparameters, and therefore expressing a unique individual body posturehave been implemented and tested. In benchmark tests on a 1.6 GHzPentium-M notebook PC, this embodiment was able to evaluate 14,000complete body postures per second. When displayed with OpenGL renderingof each actor, animation rates for 1000 actors at 9 frames per second,and for 500 actors at 18 frames per second are measured.

Using in Conjunction with Other Prior Work

The mechanism described herein is highly complementary to run-timeanimation engines that blend and overlay movement parameters throughtime with various degrees of transparency, such as the Improv Systemdescribed by [PERLIN, K., and GOLDBERG, A., 1996. Improv: A System forScripting Interactive Actors in Virtual Worlds, In Proceedings of ACMSIGGRAPH 1996 ACM Press/ACM SIGGRAPH, New York. Computer GraphicsProceedings, Annual Conference Series, ACM, incorporated by referenceherein].

It is also straightforward to combine the mechanism described hereinwith a post-process refinement or energy minimization algorithm, such asthose of [KO, H. and BADLER, N., 1996. Animating Human Locomotion inReal-time using Inverse Dynamics, Balance and Comfort Control. IEEEComputer Graphics and Applications, 16(2):50-59; COHEN, M., 1992.Interactive spacetime control for animation. In Computer Graphics(Proceedings of ACM SIGGRAPH 92), 26, 4, ACM, 293-302; GLEICHER, M.,1997. Motion editing with spacetime constraints. In Proc. of Symposiumon Interactive 3D Graphics, all of which are incorporated by referenceherein] and their successors, as well as adjustment by model-basedterrain-following foot-step placement algorithms such as those of[CHUNG, S., and HAHN J., 1999. Animation of Human Walking in VirtualEnvironments. In Proc. Int. Conf. on Computer Animation, pages 4-15.IEEE, incorporated by reference herein]. In such a combination, themechanism presented herein could be used for interactive placement andchoreography of figures, with complementary post-processing techniquesbeing applied off-line for final animation productions.

An enabling mechanism has been described that unifies foot placementwith kinematic control of an ambulatory virtual humanoid actor. The samemechanism can be generalized to quadruped, hexapod, octopod virtualactors, and so forth, by replacing the single pair of feet with multiplepairs of feet. One benefit of the described mechanism is that theunification of foot placement and body posture makes it much easier forprogrammers to create procedural mechanism for expressing body languagethat are intuitive and useful for use by artists. The resultingmechanism always produces foot placement that is well matched to bodyposture. This mechanism also allows all aspects of body posture to becomputed with low computational expense. This computation can beperformed independently for any point in time. The mechanism is wellsuited to real-time simulations containing hundreds of virtual actors,in which each virtual actor possesses expressive and responsive bodyposture customized for its particular simulated identity, personalityand situation.

This mechanism can be very effectively combined with behavioral level ofdetail, in which foreground actors are articulated with greaterfidelity, and background actors, which are smaller in the camera frame,are articulated more approximately. Behavioral level of detail is usefulbecause beyond the first several hundred actors, members of a simulatedcrowd who appear in a wide shot effectively appear as indistinct blobs.When used together with variable level of behavioral detail, themechanism described herein could support real-time responsive emotivelyexpressive behavior for crowds of essentially unlimited size, oncommodity level computers.

The mechanism described herein is also compatible with techniques thatenforce physical realism through constraints on parameter settings. Inone embodiment, energy costs of various transitions can be computedoff-line, and used to train a corpus-based method such as ConvolutionNetworks that recognizes time-series patterns [LECUN, Y. and BENGIO, Y.,1995. Convolutional Networks for Images, Speech, and Time-Series, in TheHandbook of Brain Theory and Neural Networks, (M. A. Arbib, ed.),incorporated by reference herein], to identify desired correlationsbetween parameter values in successive keyframes. For example, justbefore an actor leaps high in the air, the previous keyframe can beconstrained to consistently brace for the jump by crouching. Adding suchpre-filters does not compromise the computational speed of the describedmechanism; the combination of the described mechanism with corpus-basedtrainable methods is useful for applications that require physicalrealism.

There are numerous commercial software packages that enable characteranimation of bipeds. The following are representative and well known.

Company Product Name Alias Maya SoftImage SoftImage Discreet 3D StudioMax Character Studio Rad Game Tools Granny

All of these packages enable the bipedal virtual actor structure that isdescribed in the background material. None of them use the new temporalphase shifting.

Although the invention has been described in detail in the foregoingembodiments for the purpose of illustration, it is to be understood thatsuch detail is solely for that purpose and that variations can be madetherein by those skilled in the art without departing from the spiritand scope of the invention except as it may be described by thefollowing claims.

What is claimed is:
 1. A method for creating a computer simulation of acrowd simulation CARRIED OUT BY A COMPUTER comprising the computergenerated steps of: articulating a crowd of virtual actors withoutcollisions; having each walking virtual actor follow an output positionof a corresponding agent in A.I. that directs the crowd; and displayingthe computer simulation.
 2. An apparatus for creating a computersimulation of an actor comprising: a computer; and a software programdisposed on a computer readable medium that is run by the computer whichthen performs the computer generated steps of: depicting the actor basedon a plurality of postural parameters of the actor which include how farapart the actor's feet are, a degree of bending of the actor's knees,how far back the actor's shoulders are, and how much the actor's hipsare swaying from side to side when the actor is walking; and changingthe position of the actor.
 3. A method for creating a computersimulation of an actor having a first foot, a second foot and a bodycomprising the steps of: planting the first foot as a support foot alonga space time-varying path; stopping time regarding placement of thefirst foot; changing posture of the first foot while the first foot isplanted; and moving time into the future for the second foot as a liftedfoot and changing posture for the lifted foot.